Weighted symmetrization results for a problem with variable Robin parameter
A. Alvino, F. Chiacchio, C. Nitsch, C. Trombetti
TL;DR
This paper develops weighted rearrangement techniques to establish bounds and inequalities for solutions to Robin boundary problems with variable parameters, extending classical results like Faber-Krahn inequalities.
Contribution
It introduces a novel weighted symmetrization approach to derive a priori bounds and Faber-Krahn type inequalities for Robin problems with variable parameters.
Findings
Derived new a priori bounds for Robin problem solutions.
Established a family of Faber-Krahn type inequalities.
Extended classical inequalities to variable Robin parameter settings.
Abstract
By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Inequalities and Applications · Analytic and geometric function theory